Abstract
Counterfactuals are often described as 'retrospective,' focusing on hypothetical alternatives to a realized past. This description relates to an often implicit assumption about the structure and stability of exogenous variables in the system being modeled --- an assumption that is reasonable in many settings where counterfactuals are used. In this work, we consider cases where we might reasonably make a different assumption about exogenous variables; namely, that the exogenous noise terms of each unit do exhibit some unit-specific structure and/or stability. This leads us to a different use of counterfactuals --- a forward-looking rather than retrospective counterfactual. We introduce "counterfactual treatment choice," a type of treatment choice problem that motivates using forward-looking counterfactuals. We then explore how mismatches between interventional versus forward-looking counterfactual approaches to treatment choice, consistent with different assumptions about exogenous noise, can lead to counterintuitive results.
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